In a medium bowl, combine the vinegar with 1/4 cup of the sugar and half of the garlic and chiles. Add the carrots and let stand at room temperature for 1 hour.

Meanwhile, in a bowl, combine the lime and tangerine juices, shallot, fish sauce, sambal oelek, and water. Stir in the remaining garlic, chiles, and 1 tablespoon of sugar.

In a very large bowl, combine the green mango, cucumbers, watercress, basil, mint, and cilantro. Drain the carrots, shaking off the excess liquid, and add them to the bowl. Add the dressing and toss well. Transfer the salad to plates and mound the crab on top. Garnish with the scallions and serve.